Rate consts. for the reactions of H atoms with I2(k1) and HI(k2) were detd. in a discharge flow system using the detection of H-atoms by Lyman-a resonance fluorescence. Temp. dependent measurements in the range 250-420 K for H + I2 show an extremely weak variation with temp., k1 = (6.6 +- 3) * 10-10 exp(-20 K/T) cm3 mol.-1 s-1, which is equally well represented by the temp. independent expression k1 = (6 +- 2.5) * 10-10 cm3 mol-1 s-1. From rate measurements for H + HI in the range 250-370 K, the Arrhenius expression k2 = (7.4 +- 2.0) * 10-11 exp(-290 K/T) cm3 mol.-1 s-1 is obtained.